Internal problem ID [4126]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.4, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-\left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-y(x)=sin(x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\frac {\left (\cos ^{2}\relax (x )\right )}{5}-\frac {3}{5} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 30
DSolve[y''[x]-y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} (\cos (2 x)-5)+c_1 e^x+c_2 e^{-x} \\ \end{align*}